document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155098>Question 155098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114200 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=114200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find a quadratic equation where f(2)=16 and the minimum value of f is f(-2)=-16<BR>\n" );
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document.write( "Plot those points and you will see that f(-6) = 16 by symmetry about <BR>\n" );
document.write( "the x-axis<BR>\n" );
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document.write( "So you have three points: (-6,16),(-2,-16),(2,16)<BR>\n" );
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document.write( "Substitute these into ax^2 + bx + c = y<BR>\n" );
document.write( "to get three equations with unknowns a,b, and c.<BR>\n" );
document.write( "36a -6b + c = 16<BR>\n" );
document.write( " 4a -2b + c =-16<BR>\n" );
document.write( "4a  +2b + c = 16<BR>\n" );
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document.write( "Use any method to solve this system to get:<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = 8<BR>\n" );
document.write( "c =-8<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "y = 2x^2 + 8x -8<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.   </SPAN>\n" );
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